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From prior posts, it is obvious that Stmt 1 & 2 is insufficient. Combining, we could take X^2 is 7, hence x would be sqrt(7), which is between 1 & 4. However this would make 'y' a fraction (42/5).

Please explain this to me.

If 1 < x < 4 then for what values of X will we have x^2 as an integer? I think I am not understanding this point here.

There are 2 constraints here.
1) 1 < x < 4 and
2) x^2 is an integer

Lets take x = 1, then x^2 is also 1. If x = 4, then x^2 is 16. However the question did not mention that x is an integer. It mentions only x^2 is an integer, which means x^2 = 2,3,4 ... 15. In this case, x = sqrt2, sqrt3, sqrt4 = 2, and so on. We cannot take negative values here because of (1).